The question of the existence of active tidal disruption around various dSph galaxies remains controversial. That debate often centers on the nature (bound vs. unbound) of extended populations of stars. However, the more fundamental issue of the very existence of the extended populations is still contentious. We present an evaluation of the debate centering on one particular dSph, Carina, for which claims both for and against the existence of stars beyond the King radius have been made. Our review includes an examination of all previous studies bearing on the Carina radial profile and shows that the survey method which achieves the highest detected dSph signal-to-background in the outer parts of the galaxy is the Washington M, T2 + DDO51 (MTD) filter approach from Paper II in this series. We then address statistical methods used to evaluate the reliability of MTD surveys in the presence of photometric errors and for which a new, a posteriori statistical analysis methodology is provided. Finally, these statistical methods are tested by new spectroscopy of stars in the MTD-selected Carina candidate sample. Of 74 candidate giants with follow-up spectroscopy, the MTD technique identified 61 new Carina members, including 8 stars outside the King radius. From a sample of 29 stars not initially identified as candidate Carina giants but that lie just outside of our selection criteria, 12 have radial velocities consistent with membership, including 5 extratidal stars. Carina is shown to have an extended population of giant stars extending to a major axis radius of 40 (1.44x the nominal King radius).
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